INFM 718A / LBSC 705 Information For Decision Making

Lecture 1

Overview

• Introduction

• Aspects of decision making

• Math refresher

• Decision making process

• Modeling for decision making

• Break-even analysis

Questions

• What information did you need to make the decision?

• How did you define and compare the options?

• Are you sure your choice is the best choice?

• Are you sure your choice will stay the best choice? For how long?

Questions

• What else would you like to have known before making the decision?

• How did you feel while making the decision?

• How did you feel after making the decision?

• How do you feel now about your decision?

Decision-Making and Problem-Solving

» Define the problem

» Identify the alternatives

» Determine the criteria

» Evaluate the alternatives

» Choose an alternative

» Implement the decision

» Evaluate the results

ProblemSolving

DecisionMaking

Decision

Math Refresher

• Coordinate System, Quadrants

• Graphing Linear Equations

• Slope of a Line

• Solving Linear Equation Systems– Graphing– Substituting– Addition

Coordinate System(x, y)

Quadrants(x, y)

Graphing Linear Equations

• Example: x + 2y = 6

• Assign values to y and calculate x, based on the given y value.

• y = 0 x = 6 (6, 0)

• y = 1 x = 4 (4, 1)

• y = 2 x = 2 (2, 2)

• y = 3 x = 0 (0, 3)

• Plot these points on the coordinate system

Graphing Linear Equations

• Example: x + 2y = 6

Examples

• Plot 2x - y = 8

• Plot x = 2y - 10

Slope of a Line

• Pick two points, and find the changes in x and y.

• Use the formula to calculate slope.

xinchange

yinchangeslope

Slope of a Line

• Example: x + 2y = 6

• Points: (6, 0) and (4, 1)– change in x = 6 - 4 = 2– change in y = 0 - 1 = -1– slope = -1/2

– y = mx + b y = -1/2 x + 3

slope y-intercept

y-Intercept

• Example: x + 2y = 6

y-intercept

Examples

• What is the slope of 2x - y = 8?

• What is the y-intercept?

Examples

• What is the equation for this line:

Solving Linear Equation Systems

• Graphing

• Substituting

• Addition

• Example:

3x + 2y = 16

x - y = 2

Graphing

Solution (4, 2)

3x + 2y = 16

x - y = 2

Substituting

3x + 2y = 16 x - y = 2

x = y+23 (y+2) + 2y = 163y + 6 + 2y = 165y = 16 - 6 = 10

y = 10/5 = 2 x = y + 2 = 2 + 2 = 4

Addition

3x + 2y = 16

x - y = 2 (multiply by 2)

3x + 2y = 16

+ 2x - 2y = 4 (add two lines)

5x = 20

x = 4

y = 2

Modeling for Decision-Making

Uncontrollable Inputs(Constraints, etc.)

Controllable Inputs(Decision Variables)

Mathematical ModelOutput

(Projected Results)

Break-even Analysis

Break-even Analysis

• a: Revenue (income) per unit• B: Total fixed costs• c: Variable cost per unit• Q: number of units produced at BE point

Break-even Analysis

• P: Total revenue at BE point• K: Total costs (fixed + variable) at BE point

QaP BQcK

Break-even Analysis

KP

BQcQa

BQca )(

)( ca

BQ

BQcQa

Break-even Analysis

• a: Revenue (income) per unit• B: Total fixed costs• c: Variable cost per unit• Q: number of units produced at BE point

)( ca

BQ

Goes Beyond Sales

• Alex has determined that his car delivers 24 miles per gallon. With a $100 tune up, the car can deliver 30 miles per gallon. The price of gas is $3/gal. Assume the gas price steady, and the benefits of the tune up permanent. When will Alex reach break-even, driving at a rate of 20 miles per day?

Goes Beyond Sales

• 4000 miles

• 200 days

• $.5 savings per day

• $82.5 net savings at the end of year one

• $182.5 savings per year thereon